A possibility for precise Weinberg angle measurement in centrosymmetric crystals with axis

TL;DR

This paper proposes a method to measure the Weinberg angle precisely using nonlinear magnetoelectric effects in centrosymmetric crystals, specifically dysprosium trifluoride, which could significantly improve current measurement sensitivities.

Contribution

It introduces a novel approach leveraging parity nonconserving interactions in specific crystals to enable precise Weinberg angle measurements, with detailed estimations for experimental conditions.

Findings

Expected magnetic induction signal of 4π M_PNC ~ 0.5×10^-11 G at B=1 T and E=10 kV/cm

The effect is detectable with current or near-future sensitivity levels

Comparison across isotopes allows for high-precision Weinberg angle determination.

Abstract

We demonstrate that parity nonconserving interaction due to the nuclear weak charge Q_W leads to nonlinear magnetoelectric effect in centrosymmetric paramagnetic crystals. It is shown that the effect exists only in crystals with special symmetry axis k. Kinematically, the correlation (correction to energy) has the form H_PNC ~ Q_W (E,[B,k])(B,k), where B and E are the external magnetic and electric fields. This gives rise to magnetic induction M_PNC ~ Q_W {k(B,[k,E]) + [k,E](B,k)}. To be specific we consider rare-earth trifluorides and, in particular, dysprosium trifluoride which looks the most suitable for experiment. We estimate the optimal temperature for the experiment to be of a few kelvin. For the magnetic field B = 1 T and the electric field E = 10 kV/cm, the expected magnetic induction is 4 \pi M_PNC = 0.5 * 10^-11 G, six orders of magnitude larger than the best sensitivity currently under discussion. Dysprosium has several stable isotopes, and so, comparison of the effects for different isotopes provides possibility for precise measurement of the Weinberg angle.